$7-$ A tool life cutting test has the following results:$-$

$\backslash$table$[[\backslash$table$[[$Cutting speed,$],[$m$/$min$]],95,110,130,145,160],[\backslash$table$[[$Tool life,$],[$min$]],60,25,13,7,4\mathrm{.}8]]$

Use this values to obtain the constants of the tool life equation.

Given the following data for the cutting conditions:$-$

Time for changing the tool $=5$min.

The cost of regrinding the tool $=10$ L$.$E$/$regrinding$.$

The initial cost of the tool $=120$ L$.$E$.$

Number of possible regrinds for one tool $=15.$

cost of running the machine $=48L.E\frac{.}{h}r.$

Find the optimum cutting velocity for minimum cost and that for maximum production output.

Find the answer with steps and drawing please